(* Content-type: application/vnd.wolfram.mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 12.0' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       158,          7]
NotebookDataLength[     32024,        905]
NotebookOptionsPosition[     26671,        812]
NotebookOutlinePosition[     27025,        828]
CellTagsIndexPosition[     26982,        825]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{

Cell[CellGroupData[{
Cell[BoxData[
 RowBox[{
  SubscriptBox["R", "1"], "=", 
  RowBox[{"R", "+", 
   RowBox[{"I", " ", "\[Omega]", " ", "L"}]}]}]], "Input",
 CellChangeTimes->{{3.781911950571226*^9, 3.781911992379648*^9}},
 CellLabel->"In[30]:=",ExpressionUUID->"2b240cb1-dd7a-43b2-990d-7afaf3e87ab2"],

Cell[BoxData[
 RowBox[{"R", "+", 
  RowBox[{"\[ImaginaryI]", " ", "L", " ", "\[Omega]"}]}]], "Output",
 CellChangeTimes->{3.7819122566124496`*^9, 3.781914080658761*^9},
 CellLabel->"Out[30]=",ExpressionUUID->"61e0a9f8-5399-424e-9c00-590c79c50c86"]
}, Open  ]],

Cell[BoxData[
 RowBox[{"ClearAll", "[", "\"\<Global`*\>\"", "]"}]], "Input",
 CellChangeTimes->{{3.781912212408558*^9, 3.7819122530270405`*^9}},
 CellLabel->"In[13]:=",ExpressionUUID->"cbd876ee-1fc7-4d1e-a76e-ba11edefa7df"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Unprotect", "[", "C", "]"}]], "Input",
 CellChangeTimes->{{3.7819120357840834`*^9, 3.7819120425848975`*^9}},
 CellLabel->"In[15]:=",ExpressionUUID->"95eb3b1d-312a-4074-8e93-b41b138b8b85"],

Cell[BoxData[
 RowBox[{"{", "}"}]], "Output",
 CellChangeTimes->{3.7819120430666103`*^9, 3.781912265311902*^9},
 CellLabel->"Out[15]=",ExpressionUUID->"6ca5cf85-5e0a-4c3c-8028-a84a121fc805"]
}, Open  ]],

Cell[BoxData[
 RowBox[{"Clear", "[", "K", "]"}]], "Input",
 CellChangeTimes->{{3.7819120273995056`*^9, 3.78191203023991*^9}, {
  3.7819121211006684`*^9, 
  3.7819121217379284`*^9}},ExpressionUUID->"f079aec6-1832-434b-a029-\
b58dc9ad7175"],

Cell[BoxData[
 RowBox[{"Clear", "[", "K", "]"}]], "Input",
 CellChangeTimes->{{3.7819121260045166`*^9, 3.78191212966026*^9}},
 CellLabel->"In[8]:=",ExpressionUUID->"be6ab33a-4dfb-4e51-aa2a-6c6f7bbfe477"],

Cell[CellGroupData[{

Cell[BoxData[""], "Input",
 CellChangeTimes->{{3.781912135321122*^9, 
  3.7819121419624157`*^9}},ExpressionUUID->"04de4ff0-f21c-4632-b5b6-\
16b4aa831919"],

Cell[BoxData["K"], "Output",
 CellChangeTimes->{3.7819121359933248`*^9},
 CellLabel->"Out[9]=",ExpressionUUID->"b245c6a0-1111-42a2-bd0c-7bfb38b050d5"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  SubscriptBox["R", "2"], "=", 
  RowBox[{
   RowBox[{"-", "I"}], " ", 
   RowBox[{"1", "/", 
    RowBox[{"(", 
     RowBox[{"\[Omega]", " ", "C"}], ")"}]}]}]}]], "Input",
 CellChangeTimes->{{3.7819120020876865`*^9, 3.7819120531990213`*^9}, {
  3.781912146473298*^9, 3.7819121471784143`*^9}, {3.78191226075698*^9, 
  3.7819122614276934`*^9}},
 CellLabel->"In[31]:=",ExpressionUUID->"449b6702-861c-42a2-85f7-b4610063f273"],

Cell[BoxData[
 RowBox[{"-", 
  FractionBox["\[ImaginaryI]", 
   RowBox[{"C", " ", "\[Omega]"}]]}]], "Output",
 CellChangeTimes->{{3.781912046950224*^9, 3.7819120545414605`*^9}, 
   3.7819121581181583`*^9, 3.781912271067631*^9, 3.7819140866375656`*^9},
 CellLabel->"Out[31]=",ExpressionUUID->"3d6895f5-40be-4f19-b0a0-746851dd73ee"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"R0", "=", 
  RowBox[{
   SubscriptBox["R", "1"], " ", 
   RowBox[{
    SubscriptBox["R", "2"], "/", 
    RowBox[{"(", 
     RowBox[{
      SubscriptBox["R", "1"], "+", 
      SubscriptBox["R", "2"]}], ")"}]}]}]}]], "Input",
 CellChangeTimes->{{3.7819120711455464`*^9, 3.781912098633713*^9}, 
   3.7819122053873343`*^9},
 CellLabel->"In[32]:=",ExpressionUUID->"9e21a1ed-4364-4b41-b7ac-fa201694ab03"],

Cell[BoxData[
 RowBox[{"-", 
  FractionBox[
   RowBox[{"\[ImaginaryI]", " ", 
    RowBox[{"(", 
     RowBox[{"R", "+", 
      RowBox[{"\[ImaginaryI]", " ", "L", " ", "\[Omega]"}]}], ")"}]}], 
   RowBox[{"C", " ", "\[Omega]", " ", 
    RowBox[{"(", 
     RowBox[{"R", "-", 
      FractionBox["\[ImaginaryI]", 
       RowBox[{"C", " ", "\[Omega]"}]], "+", 
      RowBox[{"\[ImaginaryI]", " ", "L", " ", "\[Omega]"}]}], 
     ")"}]}]]}]], "Output",
 CellChangeTimes->{3.78191409052684*^9},
 CellLabel->"Out[32]=",ExpressionUUID->"5266834e-7d6e-492b-a34d-3cae94e61391"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Simplify", "[", 
  RowBox[{
   RowBox[{"-", 
    FractionBox[
     RowBox[{"\[ImaginaryI]", " ", 
      RowBox[{"(", 
       RowBox[{"R", "+", 
        RowBox[{"\[ImaginaryI]", " ", "L", " ", "\[Omega]"}]}], ")"}]}], 
     RowBox[{"C", " ", "\[Omega]", " ", 
      RowBox[{"(", 
       RowBox[{"R", "-", 
        FractionBox["\[ImaginaryI]", 
         RowBox[{"C", " ", "\[Omega]"}]], "+", 
        RowBox[{"\[ImaginaryI]", " ", "L", " ", "\[Omega]"}]}], ")"}]}]]}], 
   ",", 
   RowBox[{
    RowBox[{"{", 
     RowBox[{"R", ",", "\[Omega]", ",", "L", ",", "C"}], "}"}], "\[Element]", 
    "Reals"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.7819122877613196`*^9, 3.781912296978668*^9}, {
   3.7819130086644564`*^9, 3.781913031064554*^9}, {3.7819130738610115`*^9, 
   3.7819130853173757`*^9}, 3.781913115508149*^9},
 CellLabel->"In[33]:=",ExpressionUUID->"a9154478-be88-45ef-9bf4-14d204460461"],

Cell[BoxData[
 FractionBox[
  RowBox[{
   RowBox[{
    RowBox[{"-", "\[ImaginaryI]"}], " ", "R"}], "+", 
   RowBox[{"L", " ", "\[Omega]"}]}], 
  RowBox[{
   RowBox[{"-", "\[ImaginaryI]"}], "+", 
   RowBox[{"C", " ", "\[Omega]", " ", 
    RowBox[{"(", 
     RowBox[{"R", "+", 
      RowBox[{"\[ImaginaryI]", " ", "L", " ", "\[Omega]"}]}], 
     ")"}]}]}]]], "Output",
 CellChangeTimes->{3.781914106388034*^9},
 CellLabel->"Out[33]=",ExpressionUUID->"46d2525d-d4f9-48e7-99e2-6c5b92a1398b"]
}, Open  ]],

Cell[BoxData[
 RowBox[{"Assuming", "[", 
  RowBox[{
   RowBox[{
    RowBox[{"{", 
     RowBox[{"R", ",", "\[Omega]", ",", "L", ",", "C"}], "}"}], "\[Element]", 
    "Reals"}], ",", 
   RowBox[{"Im", "[", 
    FractionBox[
     RowBox[{
      RowBox[{
       RowBox[{"-", "\[ImaginaryI]"}], " ", "R"}], "+", 
      RowBox[{"L", " ", "\[Omega]"}]}], 
     RowBox[{
      RowBox[{"-", "\[ImaginaryI]"}], "+", 
      RowBox[{"C", " ", "\[Omega]", " ", 
       RowBox[{"(", 
        RowBox[{"R", "+", 
         RowBox[{"\[ImaginaryI]", " ", "L", " ", "\[Omega]"}]}], ")"}]}]}]], 
    "]"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.7819131322882767`*^9, 3.781913134396637*^9}, {
  3.7819132292195463`*^9, 3.7819132508928146`*^9}},
 CellLabel->"In[28]:=",ExpressionUUID->"185b4688-6a02-41ea-9100-7dad7e491af1"],

Cell[BoxData[
 RowBox[{"ComplexExpand", "[", 
  FractionBox[
   RowBox[{
    RowBox[{
     RowBox[{"-", "\[ImaginaryI]"}], " ", "R"}], "+", 
    RowBox[{"L", " ", "\[Omega]"}]}], 
   RowBox[{
    RowBox[{"-", "\[ImaginaryI]"}], "+", 
    RowBox[{"C", " ", "\[Omega]", " ", 
     RowBox[{"(", 
      RowBox[{"R", "+", 
       RowBox[{"\[ImaginaryI]", " ", "L", " ", "\[Omega]"}]}], ")"}]}]}]], 
  "]"}]], "Input",
 CellChangeTimes->{{3.781913900080847*^9, 3.781913906650885*^9}},
 CellLabel->"In[35]:=",ExpressionUUID->"d5d959d3-8409-4621-9b1c-fa06e1ec2f8f"],

Cell[BoxData[
 RowBox[{"Im", "[", 
  RowBox[{
   FractionBox["R", 
    RowBox[{
     RowBox[{
      SuperscriptBox["C", "2"], " ", 
      SuperscriptBox["R", "2"], " ", 
      SuperscriptBox["\[Omega]", "2"]}], "+", 
     SuperscriptBox[
      RowBox[{"(", 
       RowBox[{
        RowBox[{"-", "1"}], "+", 
        RowBox[{"C", " ", "L", " ", 
         SuperscriptBox["\[Omega]", "2"]}]}], ")"}], "2"]}]], "+", 
   RowBox[{"\[ImaginaryI]", " ", 
    RowBox[{"(", 
     RowBox[{
      FractionBox[
       RowBox[{"L", " ", "\[Omega]"}], 
       RowBox[{
        RowBox[{
         SuperscriptBox["C", "2"], " ", 
         SuperscriptBox["R", "2"], " ", 
         SuperscriptBox["\[Omega]", "2"]}], "+", 
        SuperscriptBox[
         RowBox[{"(", 
          RowBox[{
           RowBox[{"-", "1"}], "+", 
           RowBox[{"C", " ", "L", " ", 
            SuperscriptBox["\[Omega]", "2"]}]}], ")"}], "2"]}]], "-", 
      FractionBox[
       RowBox[{"C", " ", 
        SuperscriptBox["R", "2"], " ", "\[Omega]"}], 
       RowBox[{
        RowBox[{
         SuperscriptBox["C", "2"], " ", 
         SuperscriptBox["R", "2"], " ", 
         SuperscriptBox["\[Omega]", "2"]}], "+", 
        SuperscriptBox[
         RowBox[{"(", 
          RowBox[{
           RowBox[{"-", "1"}], "+", 
           RowBox[{"C", " ", "L", " ", 
            SuperscriptBox["\[Omega]", "2"]}]}], ")"}], "2"]}]], "-", 
      FractionBox[
       RowBox[{"C", " ", 
        SuperscriptBox["L", "2"], " ", 
        SuperscriptBox["\[Omega]", "3"]}], 
       RowBox[{
        RowBox[{
         SuperscriptBox["C", "2"], " ", 
         SuperscriptBox["R", "2"], " ", 
         SuperscriptBox["\[Omega]", "2"]}], "+", 
        SuperscriptBox[
         RowBox[{"(", 
          RowBox[{
           RowBox[{"-", "1"}], "+", 
           RowBox[{"C", " ", "L", " ", 
            SuperscriptBox["\[Omega]", "2"]}]}], ")"}], "2"]}]]}], ")"}]}]}], 
  "]"}]], "Input",
 CellChangeTimes->{{3.7819141342625337`*^9, 3.7819141381845713`*^9}},
 CellLabel->"In[36]:=",ExpressionUUID->"e166535d-4669-4e38-932c-2f32389e781c"],

Cell[BoxData[
 RowBox[{"A", "=", 
  FractionBox["R", 
   RowBox[{
    RowBox[{
     SuperscriptBox["C", "2"], " ", 
     SuperscriptBox["R", "2"], " ", 
     SuperscriptBox["\[Omega]", "2"]}], "+", 
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{
       RowBox[{"-", "1"}], "+", 
       RowBox[{"C", " ", "L", " ", 
        SuperscriptBox["\[Omega]", "2"]}]}], ")"}], "2"]}]]}]], "Input",
 CellChangeTimes->{{3.7819144029448333`*^9, 3.781914405772566*^9}},
 CellLabel->"In[37]:=",ExpressionUUID->"e1000820-fb54-4935-96c1-feafdb2f2e09"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"B", "=", 
  RowBox[{"(", 
   RowBox[{
    FractionBox[
     RowBox[{"L", " ", "\[Omega]"}], 
     RowBox[{
      RowBox[{
       SuperscriptBox["C", "2"], " ", 
       SuperscriptBox["R", "2"], " ", 
       SuperscriptBox["\[Omega]", "2"]}], "+", 
      SuperscriptBox[
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "1"}], "+", 
         RowBox[{"C", " ", "L", " ", 
          SuperscriptBox["\[Omega]", "2"]}]}], ")"}], "2"]}]], "-", 
    FractionBox[
     RowBox[{"C", " ", 
      SuperscriptBox["R", "2"], " ", "\[Omega]"}], 
     RowBox[{
      RowBox[{
       SuperscriptBox["C", "2"], " ", 
       SuperscriptBox["R", "2"], " ", 
       SuperscriptBox["\[Omega]", "2"]}], "+", 
      SuperscriptBox[
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "1"}], "+", 
         RowBox[{"C", " ", "L", " ", 
          SuperscriptBox["\[Omega]", "2"]}]}], ")"}], "2"]}]], "-", 
    FractionBox[
     RowBox[{"C", " ", 
      SuperscriptBox["L", "2"], " ", 
      SuperscriptBox["\[Omega]", "3"]}], 
     RowBox[{
      RowBox[{
       SuperscriptBox["C", "2"], " ", 
       SuperscriptBox["R", "2"], " ", 
       SuperscriptBox["\[Omega]", "2"]}], "+", 
      SuperscriptBox[
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", "1"}], "+", 
         RowBox[{"C", " ", "L", " ", 
          SuperscriptBox["\[Omega]", "2"]}]}], ")"}], "2"]}]]}], 
   ")"}]}]], "Input",
 CellChangeTimes->{{3.7819144208852644`*^9, 3.781914423365143*^9}},
 FontWeight->"Plain",
 CellLabel->"In[38]:=",ExpressionUUID->"fcb64bb3-21e6-4d01-939f-f809e45b3431"],

Cell[BoxData[
 RowBox[{
  FractionBox[
   RowBox[{"L", " ", "\[Omega]"}], 
   RowBox[{
    RowBox[{
     SuperscriptBox["C", "2"], " ", 
     SuperscriptBox["R", "2"], " ", 
     SuperscriptBox["\[Omega]", "2"]}], "+", 
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{
       RowBox[{"-", "1"}], "+", 
       RowBox[{"C", " ", "L", " ", 
        SuperscriptBox["\[Omega]", "2"]}]}], ")"}], "2"]}]], "-", 
  FractionBox[
   RowBox[{"C", " ", 
    SuperscriptBox["R", "2"], " ", "\[Omega]"}], 
   RowBox[{
    RowBox[{
     SuperscriptBox["C", "2"], " ", 
     SuperscriptBox["R", "2"], " ", 
     SuperscriptBox["\[Omega]", "2"]}], "+", 
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{
       RowBox[{"-", "1"}], "+", 
       RowBox[{"C", " ", "L", " ", 
        SuperscriptBox["\[Omega]", "2"]}]}], ")"}], "2"]}]], "-", 
  FractionBox[
   RowBox[{"C", " ", 
    SuperscriptBox["L", "2"], " ", 
    SuperscriptBox["\[Omega]", "3"]}], 
   RowBox[{
    RowBox[{
     SuperscriptBox["C", "2"], " ", 
     SuperscriptBox["R", "2"], " ", 
     SuperscriptBox["\[Omega]", "2"]}], "+", 
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{
       RowBox[{"-", "1"}], "+", 
       RowBox[{"C", " ", "L", " ", 
        SuperscriptBox["\[Omega]", "2"]}]}], ")"}], "2"]}]]}]], "Output",
 CellChangeTimes->{
  3.781914138806729*^9, {3.7819144065597677`*^9, 3.7819144244397078`*^9}},
 CellLabel->"Out[38]=",ExpressionUUID->"cba46d42-e3df-4d84-91c6-4dce1381dc20"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"A", "/", "B"}]], "Input",
 CellChangeTimes->{{3.781914434821018*^9, 3.781914438801698*^9}},
 CellLabel->"In[39]:=",ExpressionUUID->"85a2138a-83d0-4731-9aef-68b2bcc69e1a"],

Cell[BoxData[
 FractionBox["R", 
  RowBox[{
   RowBox[{"(", 
    RowBox[{
     RowBox[{
      SuperscriptBox["C", "2"], " ", 
      SuperscriptBox["R", "2"], " ", 
      SuperscriptBox["\[Omega]", "2"]}], "+", 
     SuperscriptBox[
      RowBox[{"(", 
       RowBox[{
        RowBox[{"-", "1"}], "+", 
        RowBox[{"C", " ", "L", " ", 
         SuperscriptBox["\[Omega]", "2"]}]}], ")"}], "2"]}], ")"}], " ", 
   RowBox[{"(", 
    RowBox[{
     FractionBox[
      RowBox[{"L", " ", "\[Omega]"}], 
      RowBox[{
       RowBox[{
        SuperscriptBox["C", "2"], " ", 
        SuperscriptBox["R", "2"], " ", 
        SuperscriptBox["\[Omega]", "2"]}], "+", 
       SuperscriptBox[
        RowBox[{"(", 
         RowBox[{
          RowBox[{"-", "1"}], "+", 
          RowBox[{"C", " ", "L", " ", 
           SuperscriptBox["\[Omega]", "2"]}]}], ")"}], "2"]}]], "-", 
     FractionBox[
      RowBox[{"C", " ", 
       SuperscriptBox["R", "2"], " ", "\[Omega]"}], 
      RowBox[{
       RowBox[{
        SuperscriptBox["C", "2"], " ", 
        SuperscriptBox["R", "2"], " ", 
        SuperscriptBox["\[Omega]", "2"]}], "+", 
       SuperscriptBox[
        RowBox[{"(", 
         RowBox[{
          RowBox[{"-", "1"}], "+", 
          RowBox[{"C", " ", "L", " ", 
           SuperscriptBox["\[Omega]", "2"]}]}], ")"}], "2"]}]], "-", 
     FractionBox[
      RowBox[{"C", " ", 
       SuperscriptBox["L", "2"], " ", 
       SuperscriptBox["\[Omega]", "3"]}], 
      RowBox[{
       RowBox[{
        SuperscriptBox["C", "2"], " ", 
        SuperscriptBox["R", "2"], " ", 
        SuperscriptBox["\[Omega]", "2"]}], "+", 
       SuperscriptBox[
        RowBox[{"(", 
         RowBox[{
          RowBox[{"-", "1"}], "+", 
          RowBox[{"C", " ", "L", " ", 
           SuperscriptBox["\[Omega]", "2"]}]}], ")"}], "2"]}]]}], 
    ")"}]}]]], "Output",
 CellChangeTimes->{3.781914439842499*^9},
 CellLabel->"Out[39]=",ExpressionUUID->"f3f21f6c-fa7c-4271-848a-976e7389c3a7"]
}, Open  ]],

Cell[BoxData[
 RowBox[{
  FractionBox["R", 
   RowBox[{
    RowBox[{
     SuperscriptBox["C", "2"], " ", 
     SuperscriptBox["R", "2"], " ", 
     SuperscriptBox["\[Omega]", "2"]}], "+", 
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{
       RowBox[{"-", "1"}], "+", 
       RowBox[{"C", " ", "L", " ", 
        SuperscriptBox["\[Omega]", "2"]}]}], ")"}], "2"]}]], "+", 
  RowBox[{"\[ImaginaryI]", " ", 
   RowBox[{"(", 
    RowBox[{
     FractionBox[
      RowBox[{"L", " ", "\[Omega]"}], 
      RowBox[{
       RowBox[{
        SuperscriptBox["C", "2"], " ", 
        SuperscriptBox["R", "2"], " ", 
        SuperscriptBox["\[Omega]", "2"]}], "+", 
       SuperscriptBox[
        RowBox[{"(", 
         RowBox[{
          RowBox[{"-", "1"}], "+", 
          RowBox[{"C", " ", "L", " ", 
           SuperscriptBox["\[Omega]", "2"]}]}], ")"}], "2"]}]], "-", 
     FractionBox[
      RowBox[{"C", " ", 
       SuperscriptBox["R", "2"], " ", "\[Omega]"}], 
      RowBox[{
       RowBox[{
        SuperscriptBox["C", "2"], " ", 
        SuperscriptBox["R", "2"], " ", 
        SuperscriptBox["\[Omega]", "2"]}], "+", 
       SuperscriptBox[
        RowBox[{"(", 
         RowBox[{
          RowBox[{"-", "1"}], "+", 
          RowBox[{"C", " ", "L", " ", 
           SuperscriptBox["\[Omega]", "2"]}]}], ")"}], "2"]}]], "-", 
     FractionBox[
      RowBox[{"C", " ", 
       SuperscriptBox["L", "2"], " ", 
       SuperscriptBox["\[Omega]", "3"]}], 
      RowBox[{
       RowBox[{
        SuperscriptBox["C", "2"], " ", 
        SuperscriptBox["R", "2"], " ", 
        SuperscriptBox["\[Omega]", "2"]}], "+", 
       SuperscriptBox[
        RowBox[{"(", 
         RowBox[{
          RowBox[{"-", "1"}], "+", 
          RowBox[{"C", " ", "L", " ", 
           SuperscriptBox["\[Omega]", "2"]}]}], ")"}], "2"]}]]}], ")"}]}]}]], \
"Input",
 CellChangeTimes->{{3.7819141237279468`*^9, 
  3.781914123762895*^9}},ExpressionUUID->"51e3bf8c-e6aa-4620-bdbe-\
555be353f8e1"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"ExpandAll", "[", 
  FractionBox[
   RowBox[{
    RowBox[{
     RowBox[{"-", "\[ImaginaryI]"}], " ", "R"}], "+", 
    RowBox[{"L", " ", "\[Omega]"}]}], 
   RowBox[{
    RowBox[{"-", "\[ImaginaryI]"}], "+", 
    RowBox[{"C", " ", "\[Omega]", " ", 
     RowBox[{"(", 
      RowBox[{"R", "+", 
       RowBox[{"\[ImaginaryI]", " ", "L", " ", "\[Omega]"}]}], ")"}]}]}]], 
  "]"}]], "Input",
 CellChangeTimes->{{3.7819123867577186`*^9, 3.781912460667989*^9}},
 CellLabel->"In[25]:=",ExpressionUUID->"60e7a386-259f-4cd4-a9f4-da2a83e016a1"],

Cell[BoxData[
 RowBox[{
  RowBox[{"-", 
   FractionBox[
    RowBox[{"\[ImaginaryI]", " ", "R"}], 
    RowBox[{
     RowBox[{"-", "\[ImaginaryI]"}], "+", 
     RowBox[{"C", " ", "R", " ", "\[Omega]"}], "+", 
     RowBox[{"\[ImaginaryI]", " ", "C", " ", "L", " ", 
      SuperscriptBox["\[Omega]", "2"]}]}]]}], "+", 
  FractionBox[
   RowBox[{"L", " ", "\[Omega]"}], 
   RowBox[{
    RowBox[{"-", "\[ImaginaryI]"}], "+", 
    RowBox[{"C", " ", "R", " ", "\[Omega]"}], "+", 
    RowBox[{"\[ImaginaryI]", " ", "C", " ", "L", " ", 
     SuperscriptBox["\[Omega]", "2"]}]}]]}]], "Output",
 CellChangeTimes->{3.781913127306597*^9},
 CellLabel->"Out[25]=",ExpressionUUID->"29c3ef5a-5cca-4069-b84f-b8dd6752ce40"]
}, Open  ]],

Cell[BoxData[
 RowBox[{"Im", "[", 
  RowBox[{
   RowBox[{"-", 
    FractionBox[
     RowBox[{"\[ImaginaryI]", " ", "R"}], 
     RowBox[{
      RowBox[{"-", "\[ImaginaryI]"}], "+", 
      RowBox[{"C", " ", "R", " ", "\[Omega]"}], "+", 
      RowBox[{"\[ImaginaryI]", " ", "C", " ", "L", " ", 
       SuperscriptBox["\[Omega]", "2"]}]}]]}], "+", 
   FractionBox[
    RowBox[{"L", " ", "\[Omega]"}], 
    RowBox[{
     RowBox[{"-", "\[ImaginaryI]"}], "+", 
     RowBox[{"C", " ", "R", " ", "\[Omega]"}], "+", 
     RowBox[{"\[ImaginaryI]", " ", "C", " ", "L", " ", 
      SuperscriptBox["\[Omega]", "2"]}]}]]}], "]"}]], "Input",
 CellChangeTimes->{{3.781912714224842*^9, 3.7819127162065554`*^9}},
 CellLabel->"In[22]:=",ExpressionUUID->"c67155b2-fbcc-4591-b9d5-31da56f8a6e9"],

Cell[BoxData[
 RowBox[{"Clear", "[", "Z", "]"}]], "Input",
 CellChangeTimes->{{3.781915703104484*^9, 3.781915706633467*^9}},
 CellLabel->"In[44]:=",ExpressionUUID->"eedcac8f-bd02-4846-9ac3-2aefd0ee660c"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Unprotect", "[", "I", "]"}]], "Input",
 CellChangeTimes->{{3.781916131769054*^9, 3.781916140399211*^9}},
 CellLabel->"In[50]:=",ExpressionUUID->"8ad845ac-2b25-4edd-94cc-398084c35d17"],

Cell[BoxData[
 TemplateBox[{
  "Protect","locked",
   "\"Symbol \\!\\(\\*RowBox[{\\\"\[ImaginaryI]\\\"}]\\) is locked.\"",2,50,
   10,27751622283742785880,"Local"},
  "MessageTemplate"]], "Message", "MSG",
 CellChangeTimes->{3.7819161416293526`*^9},
 CellLabel->
  "\:6b63\:5728\:8ba1\:7b97In[50]:=",ExpressionUUID->"4770a707-ffec-4d0b-ad85-\
ddcb0e34a8ad"],

Cell[BoxData[
 RowBox[{"{", "}"}]], "Output",
 CellChangeTimes->{3.7819161416762657`*^9},
 CellLabel->"Out[50]=",ExpressionUUID->"ec7a5917-0f86-4b1c-9ccc-4dcd3542a281"]
}, Open  ]],

Cell[BoxData[""], "Input",
 CellChangeTimes->{{3.78191614538731*^9, 
  3.7819161566151314`*^9}},ExpressionUUID->"798a08df-7169-48fd-b2d0-\
a400434296e8"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"TeXForm", "[", 
  RowBox[{"HoldForm", "[", "\[Mu]F", "]"}], "]"}]], "Input",
 CellChangeTimes->{{3.7819156017765102`*^9, 3.7819157236538715`*^9}, {
  3.781915808567609*^9, 3.7819158589797363`*^9}, {3.781916047990294*^9, 
  3.781916052577442*^9}, {3.7819160863227205`*^9, 3.781916124246925*^9}, {
  3.7819161819308434`*^9, 3.78191618775739*^9}, {3.7819174591507006`*^9, 
  3.7819174691966586`*^9}, {3.78191751771262*^9, 3.781917527590517*^9}},
 CellLabel->"In[54]:=",ExpressionUUID->"ca22084c-ad88-4568-bb5d-caf0d2422150"],

Cell["\\text{$\\mu $F}", "Output",
 CellChangeTimes->{
  3.781916053025243*^9, 3.781916091294073*^9, {3.781916163683592*^9, 
   3.7819161906955013`*^9}, 3.781917472722689*^9, 3.7819175291977577`*^9},
 CellLabel->
  "Out[54]//TeXForm=",ExpressionUUID->"9b5bc0a2-781d-4df0-9421-73b67c00ac81"]
}, Open  ]],

Cell[BoxData[" "], "Input",
 CellChangeTimes->{
  3.7819158997261066`*^9},ExpressionUUID->"e07637d2-508e-4587-82ee-\
d4382d29adf9"],

Cell["Z=\\text{Realpart}+i \\text{Imaginarypart}", "Input",
 CellChangeTimes->{{3.7819158923727727`*^9, 
  3.781915892388734*^9}},ExpressionUUID->"ddc072a7-9197-4630-88ef-\
446163e0d949"],

Cell[BoxData[""], "Input",
 CellChangeTimes->{{3.78191272652096*^9, 
  3.7819127265429015`*^9}},ExpressionUUID->"ce4663b7-a372-4058-94ce-\
2822d7e31d1d"],

Cell[BoxData[
 RowBox[{"Clear", "[", "U", "]"}]], "Input",
 CellChangeTimes->{{3.781918097324673*^9, 3.7819181039035177`*^9}},
 CellLabel->"In[55]:=",ExpressionUUID->"88d19537-7e0b-4d0b-8268-54155c4b8320"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"U", "=", 
  RowBox[{"{", 
   RowBox[{
   "230", ",", "230", ",", "230", ",", "230", ",", "232", ",", "230", ",", 
    "232", ",", "230"}], "}"}]}]], "Input",
 CellChangeTimes->{{3.7819181068208375`*^9, 3.7819181233081446`*^9}, 
   3.781918298246665*^9},
 CellLabel->"In[61]:=",ExpressionUUID->"7e026fd5-6187-4fb3-8390-2c4aca9fc0c9"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
  "230", ",", "230", ",", "230", ",", "230", ",", "232", ",", "230", ",", 
   "232", ",", "230"}], "}"}]], "Output",
 CellChangeTimes->{3.78191812403919*^9, 3.781918299654566*^9},
 CellLabel->"Out[61]=",ExpressionUUID->"655176cb-297a-4d18-bf59-b104564fa619"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"i", "=", 
  RowBox[{"{", 
   RowBox[{
   "0.34", ",", "0.27", ",", "0.25", ",", "0.20", ",", "0.16", ",", "0.23", 
    ",", "0.23", ",", "0.32"}], "\n", "}"}]}]], "Input",
 CellChangeTimes->{{3.781918134853238*^9, 3.7819181740361814`*^9}, 
   3.781918304607318*^9},
 CellLabel->"In[62]:=",ExpressionUUID->"7501dc50-2e30-45ca-80e7-b8889ea511eb"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
  "0.34`", ",", "0.27`", ",", "0.25`", ",", "0.2`", ",", "0.16`", ",", 
   "0.23`", ",", "0.23`", ",", "0.32`"}], "}"}]], "Output",
 CellChangeTimes->{{3.781918161538591*^9, 3.7819181760415955`*^9}, 
   3.7819183054518905`*^9},
 CellLabel->"Out[62]=",ExpressionUUID->"dabf4db1-eb90-4588-a943-441aec96093e"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"P", "=", 
  RowBox[{"{", 
   RowBox[{
   "30", ",", "30", ",", "29", ",", "30", ",", "32", ",", "30", ",", "30", 
    ",", "31"}], "\n", "\n", "}"}]}]], "Input",
 CellChangeTimes->{{3.7819181877746267`*^9, 3.78191822594382*^9}, 
   3.78191831144497*^9},
 CellLabel->"In[63]:=",ExpressionUUID->"f7e83b5a-2cd3-4b51-8940-cc56dc5ab9b0"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
  "30", ",", "30", ",", "29", ",", "30", ",", "32", ",", "30", ",", "30", ",",
    "31"}], "}"}]], "Output",
 CellChangeTimes->{3.7819182283397083`*^9, 3.78191831229443*^9},
 CellLabel->"Out[63]=",ExpressionUUID->"257e65b5-09fc-40a9-9e49-9688a901ed90"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"\[Phi]", "=", 
  RowBox[{"{", 
   RowBox[{
   "0.38", ",", "0.48", ",", "0.52", ",", "0.65", ",", "0.82", ",", "0.57", 
    ",", "0.57", ",", "0.43"}], "\n", "}"}]}]], "Input",
 CellChangeTimes->{{3.7819182375118537`*^9, 3.7819182777776446`*^9}, 
   3.7819183198882875`*^9},
 CellLabel->"In[64]:=",ExpressionUUID->"34121a85-d0d0-4cec-b81d-78317c6540f4"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
  "0.38`", ",", "0.48`", ",", "0.52`", ",", "0.65`", ",", "0.82`", ",", 
   "0.57`", ",", "0.57`", ",", "0.43`"}], "}"}]], "Output",
 CellChangeTimes->{3.781918279893414*^9, 3.7819183207774043`*^9},
 CellLabel->"Out[64]=",ExpressionUUID->"1a5a44c9-4a15-4c9c-81c4-b79286500b83"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"ListPlot", "[", "i", "]"}]], "Input",
 CellChangeTimes->{{3.7819183374280725`*^9, 3.7819183484425344`*^9}, {
  3.7819184116347656`*^9, 3.781918433979678*^9}},
 CellLabel->"In[66]:=",ExpressionUUID->"93f711fd-828b-4029-af37-72062eedc2cc"],

Cell[BoxData[
 GraphicsBox[{{}, {
    {RGBColor[0.368417, 0.506779, 0.709798], PointSize[0.012833333333333334`],
      AbsoluteThickness[1.6], 
     PointBox[{{1., 0.34}, {2., 0.27}, {3., 0.25}, {4., 0.2}, {5., 0.16}, {6.,
       0.23}, {7., 0.23}, {8., 0.32}}]}, {
     {RGBColor[0.368417, 0.506779, 0.709798], PointSize[
      0.012833333333333334`], AbsoluteThickness[1.6]}, {}}, {
     {RGBColor[0.368417, 0.506779, 0.709798], PointSize[
      0.012833333333333334`], AbsoluteThickness[1.6]}, {}}}, {{}, {}}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->{True, True},
  AxesLabel->{None, None},
  AxesOrigin->{0., 0},
  DisplayFunction->Identity,
  Frame->{{False, False}, {False, False}},
  FrameLabel->{{None, None}, {None, None}},
  FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
  GridLines->{None, None},
  GridLinesStyle->Directive[
    GrayLevel[0.5, 0.4]],
  Method->{
   "OptimizePlotMarkers" -> True, 
    "CoordinatesToolOptions" -> {"DisplayFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& ), "CopiedValueFunction" -> ({
        (Identity[#]& )[
         Part[#, 1]], 
        (Identity[#]& )[
         Part[#, 2]]}& )}},
  PlotRange->{{0., 8.}, {0, 0.34}},
  PlotRangeClipping->True,
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {
     Scaled[0.02], 
     Scaled[0.05]}},
  Ticks->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{{3.781918413442219*^9, 3.7819184348947697`*^9}},
 CellLabel->"Out[66]=",ExpressionUUID->"3ccb5b5f-4e1f-4f98-a790-371dd3753f99"]
}, Open  ]]
},
WindowSize->{639, 628},
WindowMargins->{{-7, Automatic}, {Automatic, 0}},
FrontEndVersion->"12.0 for Microsoft Windows (64-bit) (2019\:5e744\:67088\
\:65e5)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[CellGroupData[{
Cell[580, 22, 280, 6, 45, "Input",ExpressionUUID->"2b240cb1-dd7a-43b2-990d-7afaf3e87ab2"],
Cell[863, 30, 247, 4, 32, "Output",ExpressionUUID->"61e0a9f8-5399-424e-9c00-590c79c50c86"]
}, Open  ]],
Cell[1125, 37, 223, 3, 45, "Input",ExpressionUUID->"cbd876ee-1fc7-4d1e-a76e-ba11edefa7df"],
Cell[CellGroupData[{
Cell[1373, 44, 211, 3, 45, "Input",ExpressionUUID->"95eb3b1d-312a-4074-8e93-b41b138b8b85"],
Cell[1587, 49, 190, 3, 32, "Output",ExpressionUUID->"6ca5cf85-5e0a-4c3c-8028-a84a121fc805"]
}, Open  ]],
Cell[1792, 55, 238, 5, 45, "Input",ExpressionUUID->"f079aec6-1832-434b-a029-b58dc9ad7175"],
Cell[2033, 62, 203, 3, 45, "Input",ExpressionUUID->"be6ab33a-4dfb-4e51-aa2a-6c6f7bbfe477"],
Cell[CellGroupData[{
Cell[2261, 69, 154, 3, 28, "Input",ExpressionUUID->"04de4ff0-f21c-4632-b5b6-16b4aa831919"],
Cell[2418, 74, 150, 2, 32, "Output",ExpressionUUID->"b245c6a0-1111-42a2-bd0c-7bfb38b050d5"]
}, Open  ]],
Cell[CellGroupData[{
Cell[2605, 81, 445, 11, 45, "Input",ExpressionUUID->"449b6702-861c-42a2-85f7-b4610063f273"],
Cell[3053, 94, 330, 6, 51, "Output",ExpressionUUID->"3d6895f5-40be-4f19-b0a0-746851dd73ee"]
}, Open  ]],
Cell[CellGroupData[{
Cell[3420, 105, 422, 12, 28, "Input",ExpressionUUID->"9e21a1ed-4364-4b41-b7ac-fa201694ab03"],
Cell[3845, 119, 565, 15, 63, "Output",ExpressionUUID->"5266834e-7d6e-492b-a34d-3cae94e61391"]
}, Open  ]],
Cell[CellGroupData[{
Cell[4447, 139, 918, 23, 75, InheritFromParent,ExpressionUUID->"a9154478-be88-45ef-9bf4-14d204460461"],
Cell[5368, 164, 487, 14, 53, "Output",ExpressionUUID->"46d2525d-d4f9-48e7-99e2-6c5b92a1398b"]
}, Open  ]],
Cell[5870, 181, 804, 22, 65, InheritFromParent,ExpressionUUID->"185b4688-6a02-41ea-9100-7dad7e491af1"],
Cell[6677, 205, 557, 15, 65, InheritFromParent,ExpressionUUID->"d5d959d3-8409-4621-9b1c-fa06e1ec2f8f"],
Cell[7237, 222, 2078, 62, 112, InheritFromParent,ExpressionUUID->"e166535d-4669-4e38-932c-2f32389e781c"],
Cell[9318, 286, 541, 15, 49, "Input",ExpressionUUID->"e1000820-fb54-4935-96c1-feafdb2f2e09"],
Cell[CellGroupData[{
Cell[9884, 305, 1589, 49, 52, "Input",ExpressionUUID->"fcb64bb3-21e6-4d01-939f-f809e45b3431"],
Cell[11476, 356, 1460, 46, 56, "Output",ExpressionUUID->"cba46d42-e3df-4d84-91c6-4dce1381dc20"]
}, Open  ]],
Cell[CellGroupData[{
Cell[12973, 407, 194, 3, 28, "Input",ExpressionUUID->"85a2138a-83d0-4731-9aef-68b2bcc69e1a"],
Cell[13170, 412, 1967, 61, 73, "Output",ExpressionUUID->"f3f21f6c-fa7c-4271-848a-976e7389c3a7"]
}, Open  ]],
Cell[15152, 476, 1970, 62, 94, InheritFromParent,ExpressionUUID->"51e3bf8c-e6aa-4620-bdbe-555be353f8e1"],
Cell[CellGroupData[{
Cell[17147, 542, 555, 15, 65, InheritFromParent,ExpressionUUID->"60e7a386-259f-4cd4-a9f4-da2a83e016a1"],
Cell[17705, 559, 703, 18, 52, "Output",ExpressionUUID->"29c3ef5a-5cca-4069-b84f-b8dd6752ce40"]
}, Open  ]],
Cell[18423, 580, 772, 19, 64, InheritFromParent,ExpressionUUID->"c67155b2-fbcc-4591-b9d5-31da56f8a6e9"],
Cell[19198, 601, 203, 3, 45, "Input",ExpressionUUID->"eedcac8f-bd02-4846-9ac3-2aefd0ee660c"],
Cell[CellGroupData[{
Cell[19426, 608, 207, 3, 45, "Input",ExpressionUUID->"8ad845ac-2b25-4edd-94cc-398084c35d17"],
Cell[19636, 613, 357, 9, 24, "Message",ExpressionUUID->"4770a707-ffec-4d0b-ad85-ddcb0e34a8ad"],
Cell[19996, 624, 168, 3, 32, "Output",ExpressionUUID->"ec7a5917-0f86-4b1c-9ccc-4dcd3542a281"]
}, Open  ]],
Cell[20179, 630, 153, 3, 28, "Input",ExpressionUUID->"798a08df-7169-48fd-b2d0-a400434296e8"],
Cell[CellGroupData[{
Cell[20357, 637, 545, 8, 45, "Input",ExpressionUUID->"ca22084c-ad88-4568-bb5d-caf0d2422150"],
Cell[20905, 647, 290, 5, 46, "Output",ExpressionUUID->"9b5bc0a2-781d-4df0-9421-73b67c00ac81"]
}, Open  ]],
Cell[21210, 655, 131, 3, 28, "Input",ExpressionUUID->"e07637d2-508e-4587-82ee-d4382d29adf9"],
Cell[21344, 660, 187, 3, 28, InheritFromParent,ExpressionUUID->"ddc072a7-9197-4630-88ef-446163e0d949"],
Cell[21534, 665, 153, 3, 28, InheritFromParent,ExpressionUUID->"ce4663b7-a372-4058-94ce-2822d7e31d1d"],
Cell[21690, 670, 205, 3, 45, "Input",ExpressionUUID->"88d19537-7e0b-4d0b-8268-54155c4b8320"],
Cell[CellGroupData[{
Cell[21920, 677, 356, 8, 28, "Input",ExpressionUUID->"7e026fd5-6187-4fb3-8390-2c4aca9fc0c9"],
Cell[22279, 687, 298, 6, 32, "Output",ExpressionUUID->"655176cb-297a-4d18-bf59-b104564fa619"]
}, Open  ]],
Cell[CellGroupData[{
Cell[22614, 698, 368, 8, 48, "Input",ExpressionUUID->"7501dc50-2e30-45ca-80e7-b8889ea511eb"],
Cell[22985, 708, 346, 7, 32, "Output",ExpressionUUID->"dabf4db1-eb90-4588-a943-441aec96093e"]
}, Open  ]],
Cell[CellGroupData[{
Cell[23368, 720, 356, 8, 67, "Input",ExpressionUUID->"f7e83b5a-2cd3-4b51-8940-cc56dc5ab9b0"],
Cell[23727, 730, 292, 6, 32, "Output",ExpressionUUID->"257e65b5-09fc-40a9-9e49-9688a901ed90"]
}, Open  ]],
Cell[CellGroupData[{
Cell[24056, 741, 377, 8, 48, "Input",ExpressionUUID->"34121a85-d0d0-4cec-b81d-78317c6540f4"],
Cell[24436, 751, 317, 6, 32, "Output",ExpressionUUID->"1a5a44c9-4a15-4c9c-81c4-b79286500b83"]
}, Open  ]],
Cell[CellGroupData[{
Cell[24790, 762, 261, 4, 45, "Input",ExpressionUUID->"93f711fd-828b-4029-af37-72062eedc2cc"],
Cell[25054, 768, 1601, 41, 242, "Output",ExpressionUUID->"3ccb5b5f-4e1f-4f98-a790-371dd3753f99"]
}, Open  ]]
}
]
*)

(* End of internal cache information *)

